A Map with More than 100 Coexisting Low-period Periodic Attractors

Ulrike Feudel, Celso Grebogi, Brian R. Hunt, and James A. Yorke

Phys. Rev. E 54 (1996), 71-81.

We study the qualitative behavior of a single mechanical rotor with a small amount of damping. This system may possess an arbitrarily large number of coexisting periodic attractors if the damping is small enough. The large number of stable orbits yields a complex structure of closely interwoven basins of attraction, whose boundaries fill almost the whole state space. Most of the attractors observed have low periods, because high period stable orbits generally have basins too small to be detected. We expect the complexity described here to be even more pronounced for higher-dimensional systems, like the double rotor, for which we find more than 1000 coexisting low-period periodic attractors.

Back to my list of recent papers.

Back to my home page.